Removing External Degrees of Freedom from Transition-State Search Methods using Quaternions

TL;DR

This paper introduces a quaternion-based method to eliminate external degrees of freedom in transition-state searches, improving efficiency and accuracy in finite system calculations like nanoparticles and molecules.

Contribution

A novel quaternion algebra approach for removing external degrees of freedom in transition-state search methods, reducing computational effort and enhancing convergence.

Findings

Fewer images needed in NEB for accurate MEP representation

Significant reduction in iterations to reach convergence

Algorithms implemented in open-source ASE software

Abstract

In finite systems, such as nanoparticles and gas-phase molecules, calculations of minimum energy paths (MEPs) connecting initial and final states of transitions as well as searches for saddle points are complicated by the presence of external degrees of freedom, such as overall translation and rotation. A method based on quaternion algebra for removing the external degrees of freedom is described here and applied in calculations using two commonly used methods: the nudged elastic band (NEB) method for MEPs and the DIMER method for finding the minimum mode in minimum mode following searches of first-order saddle points. With the quaternion approach, fewer images in the NEB are needed to represent MEPs accurately. In both NEB and DIMER calculations of finite systems, the number of iterations required to reach convergence is significantly reduced. The algorithms have been implemented in the Atomic Simulation Environment (ASE) open source software.